asul, Cra

ent,

Keywords:Sediment diagenesis model

neses i

study summarised and categorised the variables, parameterisations and applications of 83 models

Models have been applied to a range of environments, however, there was no corresponding difference

the sequatic

processes than the entire overlying water column (Boudreau,

sophisticated models that parameterise and combine transportprocesses and reaction pathways, in order to explore the systemresponses of complex aquatic environments (see, for example,

developed to examine specically a range of systems and processes,rndt et al., 2013),aters (Pe~na et al.,2004; Jrgensen,

and Zheng, 2012),. In recent years,the development

sport models (see,, 2008) and devel-ce and suitability

(Bennett et al., 2013). With this context, it is therefore timely toanalyse the development and performance of a large body ofliterature that has emerged on sediment reactive transport models.

The basis of numerical sediment diagenesis models was laid outby Berner (1980) and further developed by authors such as VanCappellen et al. (1993), Van Cappellen and Wang (1995), andBoudreau (1997, 2000); readers wishing to understand the theoryof diagenesis models should begin with these publications. Thefundamentals were taken into early numerical models by authors

* Thematic Issue on Novel Approaches to Challenges in Aquatic EcosystemModelling.* Corresponding author.

Contents lists availab

Environmental Mod

journal homepage: www.els

Environmental Modelling & Software 61 (2014) 297e325E-mail address: dan.paraska@research.uwa.edu.au (D.W. Paraska).2000) and it is a hotspot for biogeochemical function. An explo-ration of the physical, chemical and biological dynamics in thisnear-surface sediment, termed early diagenesis, gives us a betterunderstanding of the natural processes that shape elementalpathways, and allows us to assess the effects of human activity,which include the disruption of nutrient, oxygen and carbon cy-cles associated with eutrophication and contamination of aquaticecosystems.

Sediment models are part of the greater group of increasingly

including marine organic matter degradation (Acarbon cycles (Mackenzie et al., 2004), hypoxic w2010), aquatic ecology (Arhonditsis and Brett,2010; Mooij et al., 2010), groundwater (Huntand heavy metal transport (Boudreau, 1999)increasing attention has been given to analysingof the features and applications of reactive tranfor example, Jakeman et al., 2006; Robson et al.oping standards for assessing their performanecology. The upper layer of the sediment can have more chemical (Luff and Moll, 2004). Reactive transport models have also beenMeta-analysisAquatic systems

1. Introduction

Chemical interactions betweencolumn are a key component of ahttp://dx.doi.org/10.1016/j.envsoft.2014.05.0111364-8152/ 2014 Elsevier Ltd. All rights reserved.include: aligning conceptual models of organic matter transformations with measurable parameters;gathering accurate data for model input and validation, including datasets that capture a range of time-scales; coupling sediment models with ecological and spatially-resolved hydrodynamic models; andmaking the models more accessible for water quality and biogeochemical modelling studies by devel-oping a consistent notation through community modelling initiatives.

2014 Elsevier Ltd. All rights reserved.

diment and the waterbiogeochemistry and

Steefel et al., 2005; Soetaert and Herman, 2008, for general works).The models of this eld are able to estimate chemical concentra-tions and reaction rates at a temporal and vertical resolution that isdifcult to reproduce with in situ or laboratory experimentationAccepted 6 May 2014Available online 7 August 2014in approach or complexity. The major challenges and opportunities for the development of the models16 April 2014 published since 1996. The choice of variables and processes used was found to be largely arbitrary.Sediment diagenesis models: Review ofopportunities*

Daniel W. Paraska a, *, Matthew R. Hipsey a, b, S. Ura Aquatic Ecodynamics, School of Earth & Environment, University of Western Australiab The Oceans Institute, University of Western Australia, Crawley, WA 6009, Australiac National Centre for Groundwater Research and Training, School of Earth and Environm

a r t i c l e i n f o

Article history:Received 8 July 2013Received in revised form

a b s t r a c t

A range of sediment diagehowever, the diversity makpproaches, challenges and

a Salmon c

wley, WA 6009, Australia

University of Western Australia, Crawley, WA 6009, Australia

is modelling approaches have been developed over the last two decades,t difcult to identify the best approach for a particular aquatic system. This

le at ScienceDirect

elling & Software

evier .com/locate/envsoft

such as Rabouille and Gaillard (1991a, b), Tromp et al. (1995),Furrer and Wehrli (1996), Dhakar and Burdige (1996) and Parkand Jaffe (1996). Of the models that were developed in thisperiod, the studies by Boudreau (1996), Van Cappellen and Wang(1996) and Soetaert et al. (1996a) have emerged as the basis formost of the numerical models developed by other authors sincethen (these three are cited 155, 294 and 201 times, respectively,in ISI Web of Knowledge, as of December 2013). The studies thatdeveloped from these three papers share some common processdescriptions and general conceptual bases (Fig. 1), however,many variations in the implementation and the increasingcomplexity of the biogeochemical processes in subsequent ap-plications have made it difcult to absorb the terminology,compare the models and identify the best approaches for a givenapplication that an aquatic ecosystem modeller entering theeld may be interested in. Further, while many of the originalmodels were intended for the coastal or open ocean, theyhave since been applied widely across the spectrum of aquaticenvironments, including from oligotrophic to eutrophic inlandand coastal waters. The connection between models purpose,structure and performance (as has been done recently for moregeneral models of P dynamics by Robson, 2014) remainsunexplored.

It is the aim of this article to conduct a review andmeta-analysisof sediment diagenesis model publications that have emerged sincethe theoretical texts and the key 1996 model applications. By doingso we aimed a) to identify commonality between the studies anddene a practical classication of commonly used approaches, b) to

2. Analysis approach and scope

We gathered 83 sediment diagenesis modelling studies from thepeer reviewed literature in the period between 1996 and 2013,which are listed after themain reference list at the end of the paper.We considered vertically multi-layered, rather than one- or two-layer models, process-based rather than empirical models and nu-merical rather than analytical models. The focus of this analysis isnot on the software codes themselves, which have been examinedby Meysman et al. (2003a), nor the numerical solution methods.

This analysis is primarily focussed on the multi-G models thatwere developed from the Gmodel of Berner (1980). Continuous-Gmodels have also been developed, in which the properties of thecomplex mixture are considered to be a function of depth, which inturn has reected organic matter age (originally by Middelburg,1989 then Boudreau and Ruddick, 1991, followed up recently byauthors such as Wallmann et al., 2008; Arndt et al., 2009; Vahataloet al., 2010; Rodriguez-Murillo et al., 2011; Gelda et al., 2013). Theadvantages of these empirical models are that they can be adjustedto t depth proles closely, they require few input parameters andthey recognise the importance of the changing reactivity of organicmatter over time, which is a factor that many other models do nottake into account (Van Cappellen et al., 1993). However, thecontinuous-G model studies generally neglect the reactions of theoxidants and other secondary and mineral reactions that areimportant in determining other environmental geochemical pro-cesses, such as the uxes of nutrients, oxygen and contaminants,and so this analysis is solely focused on multi-G models. Rather

D.W. Paraska et al. / Environmental Modelling & Software 61 (2014) 297e325298compare the model studies in the context of the questions theyaddress and study environments, c) based on the above analysis, toidentify challenges for the development and improvement ofsediment diagenesis models and opportunities for advancingmodel accuracy and performance, and d) ultimately to assist andencourage the uptake and application of these models by the widerecological modelling community.Fig. 1. Schematic of the main physical and chemical processes that cause chemical concenttherefore are included in most sediment diagenesis models. The chemicals and reaction prothan organic matter reactivity being assigned as proportional todepth or age, multi-G models have a few distinct pools each withdifferent reactivity. The origins of most of the recent multi-Gmodels can be traced back to one of three sources that had devel-oped Berner's model, based on either the CANDI model (Boudreau,1996), the STEADYSED model (Van Cappellen and Wang, 1996), orthe OMEXDIA model (Soetaert et al., 1996a). As will be explained inration and ux change in the sediment and across the sedimentewater interface, andcesses included in different studies vary widely and are shown in the following tables.

the following sections, these three sources differed originally withrespect to the choice of organic matter oxidants and rate lawparameterisation (Table 1), but subsequent studies have introducednumerous other changes.

We believe that this meta-analysis should help readers toidentify more easily how specic model applications comparewith the range of model features published to date. As will beshown below, any classication that was useful for the features ofthe models was less useful for the applications of the models, andso in order to analyse these 83 diverse studies more easily, westarted the classication of their features according to the threemajor approaches. Although there is no underlying philosophicaldifference between these approaches, the features of many of themodels are explained as a result of the historical development ofeach model from another previously-published models. Thisstudy summarises the model features, which include the con-ceptualisation of organic matter pools with respect to their reac-tivity, the choice of organic matter oxidants, the selection ofthe organic matter rate laws and parameters, and the range ofsecondary redox reactions, mineral reactions, and physical andbiophysical transport processes. For the analysis of model appli-cations, the study describes how these fundamental model com-ponents have been used in different environments and identiesapplications of the models where the effects of anthropogenicactivity have been the specic motivation. The study then assesseswhere the models have been applied with steady or dynamic

simulations, including where seasonal timescales of change havebeen examined, and where the coupling of sediment models tospatially resolved water column models has occurred. Finally, thefeatures and applications are brought together to assess thechallenges identied from the previous sections, and potentialopportunities to help improve model rigour and use by the widerscientic community are suggested.

3. Model components

Here a concise summary of the common features of numericalsediment diagenesis models is given, to provide context for theclassications used in the meta-analysis. The models have theirorigin in the general diagenetic equation, dened by Berner (1980)as the sum of chemical reactions and physical processes e advec-tion, diffusion and biological mixing:

v1frCsvt|{z}

Solid particle

concentration

change in time

DBv21frCs

vx2|{z}biodiffusion

v1furCsvx|{z}

advection

sedimentation

1frX

Rs|{z}reaction

(1)

Table 1The three major approaches to the parameterisation of organic matter oxidation. Terms are explained in Section 3.

ROM total organic matteroxidation rate

Oxidation rate due to ith oxidant ROxi Oxidation term FTEAi Inhibition term FIniFIn1 1

Approach 1i from reactions (3) to (8)ROM

P6i1 ROxi

ROxi kOMFOMFTEAi FIni for i 1e5,FTEAi

OxiKOxiOxi

; FTEA6 1* for i 2 to 6,FIni

Yi1j1

KOxj

Oxj KOxj

!**

Approach 2

i from reactions (3)e(8)

for i 1 to 5ROxi kOMFOMFTEAi FIniand

for i 1 to 58>>>< 0 when Oxi1 > LOxi1w

for i 2 to 5

FIni Yi1

1 Oxj!

Oxi

OxiOxi

O

ferenforionrametexe, 19ijsm004,h et al., 2009, Couture et al., 2010, Massoudieh et al., 2010, Reed et al., 2011a, b,inh Anh et al., 2012, Tsandev et al., 2012, Dale et al., 2013, Katsev and

en 1., 20et al

Her, So

akar

D.W. Paraska et al. / Environmental Modelling & Software 61 (2014) 297e325 299ROM P6

i1 ROxi ROx6 kOMFOM P5

i1 ROxi FTEAi >>>:1

OxiLOxi

FTEA6 1Approach 3

i from reactions(3), (4) and (9)

ROM P3

i1 ROxi

ROxi kOMFOMFOxi FIni for i 1, 2, F

for i 3;K

Approach 1

* Boudreau (1996) and Boudreau et al. (1998) use a difApproach 1 papers report the same Monod expression** Three Approach 1 studies use a simple on-off inhibit*** Classication based on organic matter oxidation pa**** Also include a term for bacterial reaction, FBact. SeeBoudreau, 1996*, Park and Jaffe, 1996**, Smith and JaffMorse, 2000, Haeckel et al., 2001, Konig et al., 2001, WWallmann, 2003, Luff and Moll, 2004, Eldridge et al., 2Eldridge and Morse, 2008, Devallois et al., 2008, DittricBektursunova and L'heureux, 2011, Dale et al., 2011, TrDittrich 2013, McCulloch et al., 2013

Approach 2 Van Cappellen and Wang 1996, Wang and van CappellFossing et al., 2004, Aguilera et al., 2005, Thullner et alJourabchi et al., 2008, Sochaczewski et al., 2008, KasihBessinger et al., 2012, Smits and Van Beek, 2013

Approach 3 Soetaert et al., 1996a, b, 1998, Middelburg et al., 1996,Sohma et al., 2004, Berg et al., 2007, Dedieu et al., 2007Pastor et al., 2011

Others Rabouille and Gaillard, 1991a**, Tromp et al., 1995, Dh

Berg et al., 1998, Rabouille et al., 2001, Archer et al., 2002,996, Rysgaard and Berg 1996, Van Den Berg et al., 2000, Berg et al., 2003,05****, Jourabchi et al., 2005, Canavan et al., 2006, 2007a**,b***,., 2008, 2009, Dale et al., 2009, Brigolin et al., 2009, 2011,

man et al., 2001, Sohma et al., 2001, Epping et al., 2002, Talin et al., 2003,hma et al., 2008, Soetaert and Middelburg 2009, Hochard et al., 2010,

and Burdige 1996, Furrer and Wehrli 1996, Hensen et al., 1997,when Oxi1 < LOxi1 and Oxi > LOxi

hen Oxi1 < LOxi1 and Oxi < LOxi

j1 LOxj

Oxi

KOxiOxi

8>>>>>>>:

O2

KO2O2

NO3KNO3NO3

KNO3O2O2KNO3O2

!

KAnoxNO3NO3KAnoxNO3

KAnoxO2

O2KAnoxO2

9>>>>=>>>>;

xi

1

for i 2, 3

FIni Yi1j1

KInj

Oxj KOxj

!

Yi1j1

1 Oxj

Oxj KInj

!

t expression for Mn and Fe reduction to that shown in Table 1 but subsequenteach oxidation pathway.term.terisation, yet could be argued to belong to another approach. See text in 3.1.3.t in 3.1.3.98**, Boudreau et al., 1998*, Park et al., 1999, Luff et al., 2000, Eldridge andan et al., 2002***, Meysman et al., 2003a, b, Regnier et al., 2003, Luff andBenoit et al., 2006, Katsev et al., 2006a, b, 2007, Morse and Eldridge 2007,Sengor et al., 2007, Dale et al., 2008, Muegler et al., 2012

A common approach for organic matter oxidation in multi-G

odean inherent property of organic matter (Middelburg, 1989;Boudreau and Ruddick, 1991). Nevertheless, the multi-Gbe approximated as a function of two distinct carbon pools(Berner, 1980; Westrich and Berner, 1984). This was criticised inearly years on the basis that the assignment of rates to fractions inmulti-G models is a result of the laboratory processes, rather thanvfCdvt|{z}

Dissolved

concentration

change in time

DBv2fCdvx2

fDSv2Cdvx2|{z}

biodiffusion and

molecular diffusion

vfyCdvx|{z}

advection

flow

aCd0 Cd|{z}irrigation

fX

Rd|{z}reaction

(2)

where Rs is a generic reaction term identier that applies to thesolid substance reactions and Rd to dissolved substance reactions, Cis a species concentration, r is sediment density, t is time, DB is thebiodiffusion coefcient,DS is themolecular diffusion coefcient, x isdepth, f is porosity, u is the rate of burial, y is the velocity of owrelative to the sediment surface, a is an irrigation constant and Cd0is the concentration of a dissolved substance at the sedimente-water interface (Berner, 1980; Van Cappellen and Wang, 1996).While the models chosen in this analysis all include equationssimilar to one (1) and (2), there are specic differences in thechemical reactions and transport processes that serve as the focusof our comparison below. There are also differences in the nu-merical discretisation, but in general, the models are solved by asemi-implicit (CrankeNicholson) scheme with an iterative solutionperformed at each step to resolve the non-linearities in the set ofcoupled reaction equations (see for example, Van Cappellen andWang, 1996; Berg et al., 1998).

3.1. Primary redox reactions of organic matter

The primary redox reactions describe the microbial oxidationof organic matter, which is one of the major processes drivingchemical changes in the sediment (Gaillard and Rabouille, 1992;Middelburg et al., 1997). The rate of oxidation directly de-termines the fate of many important constituents, such as nutri-ents and oxygen, and indirectly affects the rate of many otherprocesses, such as the secondary oxidation of by-products. Themodelling of organic matter mineralisation can be traced back toBerner's (1964) G model, where the reaction rate was dened asproportional to the organic matter concentration, rather than theoxidant concentration, thereby assuming that organic matteravailability was the primary control on the mineralisation rate. Inthe current sediment diagenesis models, this formulation has beenretained, and below we explore the inclusion of additional factorssuch as the number and reactivity of the organic matter pools, thechoice of oxidants, the different ways to parameterise rate laws,and the choice of the values for rate constants and otherparameters.

3.1.1. Organic matter types and pools

3.1.1.1. Particulate organic matter. A major challenge in modellingorganic matter oxidation has always been conceptualisation andsimplication of the reactions of thousands of different organicmolecules. The multi-G model divides organic matter intoseveral classes, based on reactivity, which are mineralised to CO2at different rates. The basis of the multi-G assumption came fromlaboratory experiments that showed organic matter decay could

D.W. Paraska et al. / Environmental M300approach has continued to be used because of its conceptualand mathematical simplicity (Boudreau and Ruddick, 1991;OM 2xMnO2 3x y 2zCO2 x y 2zH2O/2xMn2 4x y 2zHCO3 yNH4 zHPO24

(5)

OM 4xFeOH3 7x y 2zCO2 x 2zH2O/4xFe2

8x y 2zHCO3 yNH4 zHPO24 3x y 2zH2Omodels is through the sequence of reactions (3)e(8), based ongeneral observations from authors such as Froelich et al. (1979) andEmerson et al. (1980):

OM xO2 y 2zHCO3/x y 2zCO2 yNH4 zHPO24 x 2y 2zH2O (3)

OM 0:8xNO3/0:2x y 2zCO2 0:4xN2 0:8x y2zHCO3 yNH4 zHPO24 0:6x y 2zH2O H3PO4 177:2H2O

(4)Thullner et al., 2007). Of the 83 modelling studies in this anal-ysis, 22 use only one pool; 31 use two, 22 use three and two usefour. For 3G models, in general, there is a highly reactive frac-tion, a moderately reactive fraction and an unreactive fraction(Table 2). However, the variety in number of pools, rate constants,and indeed even terminology in Table 2 shows that there islimited consistency, and assignment of G type is not based on anyinherent property of organic matter.

3.1.1.2. Dissolved organic matter (DOM). While different solid phaseorganic matter fractions of varying reactivity are routinely consid-ered in sediment models, organic matter in the dissolved phase isincluded in only eight models, which have been published in thir-teen papers (Table 2). Within these, a range of techniques are used:Approach 1 models input DOM to the sediment surface as a uxfrom the water column; Approach 2 models have DOM form as aproduct of the breakdown of particulate organic matter (POM).Approach 3 papers specify the individual DOM sources, such asphytoplankton, zooplankton and benthic algae; the DOM is con-ceptualised as one or two pools that are mineralised through thesame processes as POM and transported through diffusion. DOMadsorption to solid particles has been used in three of the studies(Sohma et al., 2004, 2008; Massoudieh et al., 2010).

3.1.1.3. Microbial biomass. Most models do not consider variationin microbial biomass as a control on organic matter decay, howeversediment bacteria are included in some models as a dynamicallyvarying organic matter pool. This has been either as total bacteria(Talin et al., 2003), groups that oxidise organic matter through eachof the six pathways (Thullner et al., 2005), or assuming a steady-state biomass (Dale et al., 2008a, based on Dale et al., 2006,which explicitly models acetogenic, sulphate-reducing and fer-menting bacteria, and methane-oxidising and methanogenicarchaea reactions, but without transport processes).

3.1.2. Choice of reaction pathways

lling & Software 61 (2014) 297e325(6)

Table 2Different organic matter pools, uxes, rate constants, and stoichiometry.

Reference Fractions Flux to sediment surface

Approach 1 POMpools

DOM Pool names % Of ux, Datasource

POM uxmmol cm2 y1

kOMy1

C:N or C:N:P

Boudreau, 1996 2 e e a 18.5 12.2 105

200:21:1 for deepsea, rise, slope/shelf106:16:1Coastal

Park and Jaffe, 1996 1 Total e b 100 By O2 1NO3 0.5Mn(IV) 0.01Fe(III) 0.005SO42 0.1Meth 0.01

106:16:1

Boudreau et al., 1998 2 Highly reactiveWeakly reactive

3%, 74%, 50%97%, 26%, 50%

r No ux: xed bottomwater concentrationof OM as a fractionof solids

Various 1, 35 105, 1 103,2 103

106:22 for one site106:25 for two sites

Smith and Jaffe, 1998 1 Total e b 100 By O2 1NO3 0.04Mn(IV) 0.01Fe(III) 0.005SO42 0.17Meth 0.05

Not given

Park and Jaffe, 1999 1 Total e b 2555(Sensitivity analysis:36.5, 365, 730, 1825,3650)

By O2 10.95NO3 1.825Fe(III) 0.0365SO42 14.6Meth 0.146

106:16:1, 106:32:1,106:52:1

Luff et al., 2000 3 Extremely labileModerately labileRefractory

6e82%15e90%1e6%

e 70, 75, 55, 160, 25, 20, 10, 168, 1.2, 2, 0.7

30, 15 Extremely0.6, 0.35, 0.34, 0.2Moderately5 104, 3 104,2.2 104 Refractory

106:16:1 for allfractions

Eldridge and Morse, 2000 2 1 LabileRefractoryDOM

5.8e73%26e94%

e 51.1e678.9248.2e901.6

6.5e15.5 Labile0.06e0.3 Refractory0.25e6 DOM

105:12, 6, 9:0.2,105:4, 6, 8:0.1105:3:0.1

Haeckel et al., 2001 2 LabileRefractory

97%3%

e 12, 9, 6.50.4, 0.15

1 102, 8 103 Labile1 106, 5 106 Refr.

106:16:1 for allfractions

Konig et al., 2001 3 Very labileLabileRefractory

85%15%0.30%

e 4070.15

1, 0 Very labile8 103, 0 :Labile1 106 Refractory

106:16:1 for allfractions

Wijsman et al., 2002 3 Fast-decayingSlow-decayingRefractory

29%, alsodependent onwater depth

e Maximum 6351 27.5 Fast1.1 Slow

106:16 fast106:11 slow

Meysman et al., 2003b 3 Fast degradableMedium degradableSlowly degradable

18%16%66%

e 6760250

2 Fast0.056 Medium1.1 104 Slow

106:16:1.5 fast106:16:1.5 med265:24.5:1 slow

Luff and Wallmann, 2003 2 LabileRefractory

68%32%

e 5526

0.2 Labile3 104 Refractory

Not given

Luff and Moll, 2004 3 LabileModeratelydegradableRefractory

40%55%5%

e 60827

30 Labile0.2 Moderate5 104 Refractory

106:16:1for all

Eldridge et al., 2004 2 LabileRefractory

e 25 Labile0.12 Refractory

105:5:0.6105:4:0.6

(continued on next page)

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Table 2 (continued )

Reference Fractions Flux to sediment surface

Benoit et al., 2006 2 ReactiveautochthonousmarineLess reactiveallochthonousterrestrial

Changing alongstream fromeld data

a 100e200, 50e1100e500, 0e60

10 Reactive0.4 sedimentation^0.6Less

C:N 106:16C:N 106:8.83

Katsev et al., 2006a 1 e 100% b 1.25e5 0.9 C:P 200:1Katsev et al., 2006b 1 Reactive

(Refractory)99.6%(0.4%)

b 2.33 1021.0 104

0.1 Reactive4 105 Refractory

Not given

Katsev et al., 2007 2 ReactiveRefractory

30%70%

e 100230

1.8 Reactive0.02 Refractory

67:3.3:1250:12.5:1

Morse and Eldridge, 2007 2 1 LabileNon-labileDissolved

68%, 83%, 80%32%, 17%, 20%

e Sensitivity:791, 1034, 365365, 213, 91

20 Labile0.8 Non-labile35 Dissolved

105:25:0.158105:25:0.10105:25:0.10

Eldridge and Morse, 2008 2 2 ReactiveRelativelynon-reactiveDOMDOMI

d Taken from Morseand Eldridge, 2007

20 Reactive0.080 Relatively non-35 DOM

105:25:0.158105:25:0.10105:25:0.10

Devallois et al., 2008 1 e e b Not given 2 108 July, 2 109November

106:16:1

Dittrich et al., 2009 3 Fast degradableSlow degradableNon-degradable

30%20%50%

d 0.210.140.35

For degradable only: byO2 9.2NO3 7.3MnO2 0.04FeOOH 1.8 104SO42 0.04Meth 5.8 103

93:13:1 fast93:13:1 slow357:15:1 non

Couture et al., 2010 1 e e b Not given 400 e(0.183depth) Not givenMassoudieh et al., 2010 1 Easily mineralisable e b Not given 25 C:N 106:815Reed et al., 2011a 2 Reactive

Refractory91.5%8.5%

g 2.70.25

0.07 Reactive0 Refractory

106:30:1 reactive106:7.6:1 refractory

Reed et al., 2011b 3 Highly reactiveLess reactiveNon-reactive

50%16%34%

a Maximum 438 24 4 Highly-1.4 0.7 Less-

106:16:1290:29:1

Bektursunova andL'heureux, 2011

1 e e b Not given e Not given

Dale et al., 2011 3 G1G2G3

100%Fixedconcentration

e/g 329, 767 0.05 G11.5 103 G24.2 104 G3

C:N 106:9.5106:8106:27

Trinh Anh et al., 2012 2 DegradableRefractory

48, 57, 6352, 43, 37

a 8517, 12167, 203709125, 9125, 12167

By O2 36.5NO329.2Fe30.011SO420.29Meth 0.146

27.5:3:1 degradable60:2:1 refractory

Tsandev et al., 2012 3 Very labileModerately labileRefractory

90% d 7.5, 15 0.15 Very0.0015 ModeratelyRetardation by SO42

and Meth 7 104

200:21:1

Dale et al., 2013 4 G0G1G2G3

89%11%Fixedconcentration

e/g 5.84 G00.05G11.5 103 G 24.2 104 G3

C:N 106/9.5106/9.5106/8106/27

Katsev and Dittrich, 2013 3 ReactiveWeakly reactiveRefractory

401446

e 11440130

2 Refractory0.05 Weak0 Refractory

50:7:1

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McCulloch et al., 2013 2 DegradableRefractory

48%52%

e 1.61.7

By O2 8.8NO3 763MnO2 1.6 103FeOOH 1.2 104SO42 3.6 102

106:16:1

Approach 2 POMpools

DOM Pool names % of ux Datasource

POM uxmmol cm2 y1

kOM y1 C:N or C:N:P

Van Cappellen andWang, 1996

Rate assigned tomeasured depthprole

Wang and VanCappellen, 1996

Rate assigned tomeasured depthprole

Rysgaard and Berg, 1996 1 e e b Not given Rate by O20.0035 nmol cm3 s1

Rate by NO3

0.00058 nmol cm3 s1

106:16:1

Van Den Berg et al., 2000 1 Total OM from cores e b Not given 150, 600,950 mmol cm3 y1

at sediment-waterinterface

20:1.6:1

Berg et al., 2003 3 Fast decomposingSlow decomposingNot decaying

25%75%

a 292e1200 Calculated by depthfrom core data

Trials of 106:14,106:10.3, 106:16for all fractions

Fossing et al., 2004 3 Degraded fastDegraded slowlyNot degraded

42%50%8%

g 44553085

303 Fast0.378 Slow0

80:8:1 for allfractions

Aguilera et al., 2005 2 LabileRefractory

c 32 total 30 Labile0.3 Refractory

Not given

Jourabchi et al., 2005 1 e e b 80 0.01 200:21:1Thullner et al., 2005 1 1 Labile

DOMe b 660, 650, 635 0.95 106:12:1

Canavan et al., 2006 3 Most reactiveLess reactiveNon-reactive

42%21%37%

e 630315546

1 Most0.01 Less0

112:20:1 mostreactive200:20:1 lessreactive

Canavan et al., 2007b 3 Highly reactiveLess reactiveRefractory

42%, 33%21%, 25%37%, 43%

e 630, 420315546

25 Highly0.01Less0

106:19106:11106:5

Kasih et al., 2008 3 2 Fast degradable POMSlow degradable POMNon-degradable POMFast degradable DOMSlow degradable DOM

40%40%20%

g a 31.5 Fast0.00315 Slow0

70:8.75:1 forall fractions

Sochaczewski et al., 2008 2 Fast reactingSlow reacting

Not given c Not given 302 Fast0.378 Slow

Not given

Jourabchi et al., 2008 2 Highly degradableRefractory

50e100%(13 values)

e 4.3e29 (13 values) 1.16e10 (13 values) 106:16:1200:21:1

Kasih et al., 2009 3 2 Fast degradableSlow degradableNon-degradableFast degradableSlow degradable

40%40%20%43%57%

a 328328164

78.8 Fast0.00378 Slow0 Non

70:8.75:1 forall fractions

Dale et al., 2009 3 Fast reacting labileIntermediatereactivitySlowly reactingrefractive

53%34%12%

e 700450160

2 Fast0.03 Intermediate1.4 104 Slowly

106:11

(continued on next page)

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Table 2 (continued )

Reference Fractions Flux to sediment surface

Brigolin et al., 2009 3 RefractoryLabileSalmon farmorganic deposit

67%33%

d 9030

0.10.01

80:8:180:8:170:8:1

Brigolin et al., 2011 2 RefractoryLabile

0.40.6

a 160240

0.001 Refractory1.0 Labile

106:16:1106:16:1

Bessinger et al., 2012 1 1 e b SOM ux not givenDOC 1e10 mg/L

0.002 POM0.001 DOM

Not given

Smits and Van Beek, 2013 4 1 FastModerately slowSlowVery slowRefractory

f Calculateddynamically

Approach 3 POMpools

DOM Pool names % of ux Datasource

POM uxmmol cm2 y1

kOM y1 C:N or C:N:P

Soetaert et al., 1996a 3 Most degradableLeast degradableRefractory

74%26%

e 207, 48, 1873, 17, 6

26 Most0.26 Least0 Refractory

C:N 106:16C:N 106:14

gSoetaert et al., 1996b 2 Most reactive

Least reactive50%50%

d 32.532.5

2 Most0.02 Least

C:N 6.6C:N 7.5

Middelburg et al., 1996 2 FastSlow

Not given c Sensitivity analysis0.00365 to 365

C:N 6.6, 8C:N 10, 20

Soetaert et al., 1998 2 Highly reactiveLess degradableRefractory

70e80%0.32%

a Total 64 28.5 Highly0.03 Less

Not given

Sohma et al., 2001 2 1 Fast labileSlow labileDissolved

f 0.438 Fast8.76 103 Slow8.76 103 DOM

106:15106:15106:9.6

Herman et al., 2001 2 Fast degradingSlowly degrading

Calibrated with Monte Carlosensitivity analyses

different

Epping et al., 2002 2 DegradableRefractory

60e85% d ~11.4e189.8 0.066e7.91 Degrad.0.0002e0.319 Refr.

C:N 106:16to 106:7

Talin et al., 2003 1 e e b BW conc, no ux 14.6 Not givenSohma et al., 2004 3 2 Fast labile

Slow labileRefractoryLabileRefractory

f 4.38 Fast0.0438 Slow0.000876 Refr.8.76DOM Lab0 DOM Ref

Not given

Berg et al., 2007 2 Fast decomposingSlowly decomposing

50%50%

d Total 230 63 Fast9.5 102 Slow

Not given

Dedieu et al., 2007 2 LabileMore refractory

80, 85, 90%20, 15, 10%

e 350.4e3153.687.6e788.4

21.9, 36.5 Labile0.365 More

C:N 6.6:1C:N 10:1

Sohma et al., 2008 3 2 Fast labileSlow labileRefractoryFast labileRefractory

90%7.5%2.5%

c From the model 4.4 Fast4.4 101 Slow4.4 103 Refr8.8 DOM fast0 DOM Refr.

27.6:6.2:147.6:7.5:1500:37:125:6:1500:37:1

Soetaert andMiddelburg, 2009

2 Rapidly decayingSlowly decaying

50%50%

d or a Input by pelagicmodel

26 Rapid0.26 Slow

C:N 106:16C:N 106:14

Hochard et al., 2010 3 Labile, fast decayingStable, slow decayingEPS (labile, particulate)

38%62%

d 12612050

27.4 Labile1.1 Stable

106:16 fast106:7 slowCH2O

Pastor et al., 2011 2 Fast degradedSlow degraded

50e94% e 1.96 103 to 95.47 11, 33 Fast0.21 to 0.36 Slow

106:15 fast106:7.4 slow

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Others POMpools

DOM Poolnames

% of ux Datasource

POM uxmmol cm2 y1

kOM y1 C:N or C:N:P

Rabouille andGaillard, 1991a

1 Reactive(Inert)

100% of POC ux(0.1% of dry solids)

b 25.2, 17.3, 9.5 By O2 0.047By NO3 0.0158By Mn 1.58 1080

106:16:1

Tromp et al., 1995 2 LabileRefractory

90%10%

g/a Many sites Function ofsedimentation rate0

106:16:1

Dhakar and Burdige, 1996 1 e e b 4.2e8.5 By O2 1.3 103, 2.3 103,6.8 103NO3 6 104, 1.2 103Mn 5.2 104, 1.3 103Fe 6.5 104, 1 103

106:16:1

Furrer and Wehrli, 1996 1 e e b 620.5 Various 106:16:1Hensen et al., 1997 1 e e b Assumed excess Depth dependent C:N 106:16Rabouille et al., 2001 2 Labile

Intermediate reactivity79%, 54%21%, 46%

e 34, 14 1.6, 1.60.012, 0.008

C:N 9.3:1

Archer et al., 2002 2 LabileRefractory

50%50%

e 0e905 Proportional to sedimentdepth

Not given

Sengor et al., 2007 1 Acetate e g 7000 M 0.16 Not givenDale et al., 2008 3 Labile

IntermediateRefractorySpecic DOM molecules

95%, 25%0%, 6%5%, 9%

e 450, 1000, 2325, 270

0.22, 0.12e, 0.00350, 0(Not kOM, rather hydrolysisrate)

Not given

Dale et al., 2008 2 LabileRefractorySpecic DOM molecules

90%10%

e Not given

Muegler et al., 2012 1 1 OMpptOMred

e b 8 104 M By O2 272, Anoxic 9.86 Not given

The assignment of the organic matter reactivity fractions is given by methods a to g.(a) Assigned according to eld data: Boudreau, 1996 fromMurray and Kuivila, 1990. Berg et al., 2003 e FromWestrich and Berner 1984, Otsuki and Hanya, 1972, Rysgaard et al., 1998; Fossing et al., 2004 e Fast: from literaturevalues; Not degraded: function of sedimentation rate and bottom concentration; Benoit et al., 2006e relative uxes actually estimated in this source; Kasih et al., 2008e Total ux hasmonthly data; For the reactive particulate,cites Fossing et al., 2004 and Berg, 2003; For the dissolved, tuned in this study; Reed et al., 2011be FromWestrich and Berner 1984; Brigolin et al., 2011e Tentative, from Giordani et al., 2002; Trinh Anh et al., 2012 from TrinhAnh et al., 2006.(b) 1G.(c) Not given.(d) Proportions assigned at the outset: Soetaert et al., 1998 e Based on Soetaert et al., 1996a; Berg et al., 2007 e From Soetaert et al., 1996b; Eldridge andMorse, 2008 e Taken fromMorse and Eldridge, 2007; Kasih et al., 2009 eBased on Kasih, 2008.(e) Tuned to t a chemical depth prole or ux data from the site of the study.(f) Flux input from a coupled model.(g) Assigned by a function: Tromp et al., 1995 e From Ingall and Vancappellen, 1990 e a general rule for sediment carbon, not a site ux; Reed et al., 2011a e estimated based on primary production data from the site. Sengor etal., 2007 e concentration set to be higher than values measured at the study site, and always to be in excess.

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OM 0:5xSO24 y 2zCO2 y 2zH2O/0:5xH2S x y 2zHCO3 yNH4 zHPO24

(7)

OM y 2zH2O/0:5xCH4 0:5x y 2zCO2 y 2zHCO3 yNH4 zHPO24 (8)

where x, y and z represent the user-dened C:N:P ratios (Table 2)and OM is organic matter. The reaction stoichiometry shown hereis from Canavan et al. (2006), with most studies adoptingdifferent stoichiometric relationships. Many studies (28) use allsix pathways, however, depending on reasons specic to indi-vidual applications, any of the pathways may be left out (Table 3).A subset of the models combines the pathways in reactions

Table 3Organic matter oxidation pathways used in sediment diagenesis models.

D.W. Paraska et al. / Environmental Modelling & Software 61 (2014) 297e325306

te expat, witpprr sim

ode(5)e(8) together to produce oxygen demand units (ODU), whichare a combination of reduced-species products of the anoxic

Fig. 2. The reaction rates of each oxidation pathway compared between the three raamount of organic matter, with no further inputs, was simulated to decay via six redoxApproach 2 (Van Cappellen and Wang, 1996) and Approach 3 (Soetaert et al., 1996a)pathways to occur simultaneously, albeit at low rates for inhibited pathways, whereas Athe overall rate of mineralisation in Approach 3 as all three pathways are able to occu

D.W. Paraska et al. / Environmental Moxidation of organic matter:

OM TEA!RAnox 106ODU 106CO2 12NO3 HPO24 106H2O (9)

where TEA is a terminal electron acceptor. The models thatcombine the anoxic processes fall into the rate law formulationcategory that we dene as Approach 3, described below. The samereactions are generally applied to all organic matter pools, althoughdifferent rate constants are applied for different pools and some-times for different oxidants (see Table 2 and text below).

3.1.3. Rate law formulationMost models inspected in this analysis employ one of three

main approaches to organic matter oxidation rate laws; togetherthese three approaches have made up the bulk of depth-resolvednumerical process-based models since 1996 (Table 1). In Ap-proaches 1 and 2 the total organic matter reaction rate (ROM) is thesum of some combination of the oxidation pathways (3) to (8). InApproach 3, the total ROM is the sum of pathways (3), (4) and (9),where equation (9) combines Mn(IV), Fe(III) and SO42 reduction. Acommon feature of all three approaches is that the oxidation rateexpression ROx is a product of up to seven terms: an organic matterreaction rate constant kOM; a factor for dependence on the organicmatter concentration, FOM; a temperature dependence FTem; a mi-crobial biomass factor, FBio; a term FTEA for limitation; an inhibitionterm FIn; and a thermodynamic factor, FT (Arndt et al., 2013):

ROxi kOMFOMFTemFBioFTEAi FIni FT (10)The FTem is rarely employed, but in a handful of cases a Q10

relationship between 2 and 4 is used (see Fossing et al., 2004 for aclear explanation of how temperature affects reaction rates andEldridge and Morse, 2008 or Reed et al., 2011b for a specic ex-

pressions approaches in representative marine and freshwater conditions. An initialhways using rate constants from the original sources for Approach 1 (Boudreau, 1996),hout simulation of secondary or transport processes. Approach 1 equations allow alloach 2 equations create a more distinct inhibition sequence. There is a brief increase inultaneously at close to their maximum rate.

lling & Software 61 (2014) 297e325 307amination of the effect of temperature). The limitation term ac-counts for the ROx dependence on the oxidant concentration whenthe oxidant concentration is low. The FTEA term in Approach 1 is aMonod expression (Table 1), which uses Monod half-saturationconstants (KOx), and which is chosen because it best reects labo-ratory data of bacterially-controlled oxidation reactions (Boudreauand Westrich, 1984; Gaillard and Rabouille, 1992). The FTEA ofApproach 3 uses Monod functions, modied to include inhibitionterms. In Approach 2 the FTEA is either 0, 1 or the ratio of the con-centration of the ith oxidant (Oxi) to a specied limiting concen-tration (LOxi). We use the notation KOx and LOx to emphasise that adistinction should be made between the Monod half constants inApproaches 1 and 3 and the limiting concentrations used inApproach 2; the difference in conceptual representation is not al-ways clear in Approach 2 papers that use the notation KOx.

The redox zonation commonly observed in the sediment isimplemented in the models through inclusion of the inhibitionfactor, FIn. This term limits ROx for a pathway that yields less energywhile higher-energy pathways continue to be active. MostApproach 1 and 2 papers set KOx and KIn or LOx and LIn to have thesame value, whereas Approach 3 papers generally specify sepa-rate KOx and KIn values, as does the Approach 1 study by Coutureet al. (2010). The inhibition term FIn in Approaches 1 and 3 is aMonod function, while in Approach 2 it is the modied Monodterm, which employs Blackman kinetics (Boudreau, 1997). Theorganic matter oxidation rate expressions of the three approacheshave been compared by conducting simple experiments usingcommon boundary conditions and constants, and it has beenfound that while the overall rate of organic matter consumption islargely the same, the rates of oxidant consumption can bedifferent as a result of the rate expressions alone (Paraska et al.2011) (Fig. 2).

Table 4Secondary redox reactions implemented in sediment diagenesis models.

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odeD.W. Paraska et al. / Environmental MThe FOM term is usually a rst order dependence on organicmatter concentration, however Dhakar and Burdige (1996), Smithand Jaffe (1998), Regnier et al. (2003) and Thullner et al. (2005)(scenario three) have included a Monod limitation term:

OMOM KOM

(11)

where KOM is a half-saturation constant inducing limitation of theorganic matter breakdown rate.

The models described above that include bacteria as an organicmatter pool also include a term for the effect of bacteria FBio, whencalculating ROx. The very rare inclusion of bacteria in sedimentdiagenesis models is adapted from approaches used in ground-water models, such as the model of Schafer et al. (1998a, b). Thisapproach has been used in surface water sediment models by Talinlling & Software 61 (2014) 297e325 309et al. (2003), who compared their model to Approach 3, and byThullner et al. (2005) who compared theirs to Approach 2. In bothcases, the authors found that including bacteria makes a largerdifference under dynamic conditions than at steady state (seebelow for discussion of steady and dynamic conditions). Theexclusion of bacteria from most diagenesis models is based on theassumption that when the microbial populations are at steadystate, ROM should not be limited by the biomass (Van Cappellenet al., 1993).

Many of the early authors have referred to the work of Froelichet al. (1979), who showed not only an organic matter oxidationsequence, but also explained the sequence in terms of the freeenergy made available in each reaction. However, the most modelsdistribute the rates via the inhibition terms. The consideration offree energy as a controlling factor in the oxidation process (FT) hasmostly not been considered in sediment models, except for where

Table 5pH and mineral reactions in sediment diagenesis models.

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odeit has re-emerged in the work of Dale et al. (2008), who have builtonwork by authors such as Jin and Bethke (2002, 2003, 2005). Notehowever, that the Dale et al. (2008) model did not include many ofthe primary and secondary reactions that have been included in themajority of papers from the last two decades, thus we are yet to seea full diagenesis model that uses free energy as a controlling factorin its rate calculations. FT is usually expressed as in equation (12),where DG is the energy released upon reaction of an organicmolecule, DGATP the energy required to synthesise ATP, m and cstoichiometric coefcients, R is the gas constant and T temperature(Jin and Bethke, 2007; LaRowe and Van Cappellen, 2011; LaRoweet al., 2012).D.W. Paraska et al. / Environmental MFT 1 expDGmDGATP

cRT

(12)

The difculty in using an FT term lies in reconciling the veryspecic reaction energetics of individual molecules with theimprecise basis of kOM values used in multi-G models.

3.1.4. Choice of parameter valuesAs can be seen from the range of conceptualisations and

parameterisations discussed 2 above, the maximum rate ofdegradation, kOM (Fig. 3, Table 2), could represent a rate constantfor a wide range of different reactions, so a direct comparison ofkOM from different modelling studies remains difcult. Mostmodels have separate kOM values for each G fraction and assumethis is the same for all oxidation pathways. Some account for anincreased oxic mineralisation rate with an acceleration factor forthe faster rate of aerobic mineralisation (25 for Canavan et al.,2006; Brigolin et al., 2009; Couture et al., 2010; 10 for Daleet al., 2011; Bessinger et al., 2011), while Reed et al. (2011a, b)attenuate SO42 reduction and methanogenesis rates by1.57 103, based on eld data from Moodley et al. (2005) andTsandev et al. (2012) by 7 104. Nine studies have separateoxidation rate constant values (kOM) for each oxidant (Table 2),however, in the majority of studies, kOM represents an average ofall of the oxidation pathways and is assigned a constant value.Sourcing locally relevant parameters has been a challenge formany studies, and only in a few cases has direct measurement ofkOM been possible (for example, Boudreau, 1996; Sohma et al.,2008; Reed et al. 2011a). Most applications therefore rely on liter-ature values and/or calibration. Van Cappellen and Wang (1996)obtained their oxidation rate from sediment incubation experi-ments by Caneld et al. (1993), situated at the same study site astheir modelling study. Couture et al. (2010) measured organicmatter breakdown with depth in a sediment column and used theexperimental value for kOM in their diagenesis model. However,most studies calibrate kOM to t concentration depth proles or usean assumed value from the literature, where those that are taken

lling & Software 61 (2014) 297e325 311from previous papers have often been determined by calibration toanother dataset, rather than originating from an experimentaldetermination. Many of these can be traced back to Van CappellenandWang (1995), where several parameter values are tted to coreproles. Most papers have calibrated their depth proles against4e7 measured variables, except Approach 3 papers, where fewvariables are simulated; a few Approach 1 and 2 studies calibrate upto 16 variables (Berg et al., 2003; Fossing et al., 2004; Dittrich et al.,2009). Other kOM estimates are based on denitrication laboratoryexperiments (for example, Billen, 1978; Esteves et al., 1986; Murrayet al., 1989) and sulfate reduction experiments (Boudreau andWestrich, 1984). While some publications have consideredparameter sensitivity and identiability, detailed investigationsadopting contemporary model performance metrics (see, forexample, Bennett et al., 2013) remain limited.

Some studies (e.g., Brigolin et al., 2009, 2011) use the kOM valuedirectly from, or use the method of, Tromp et al. (1995). With thismethod, kOM is determined using a statistical relationship betweenu (burial) and 22 measured organic matter degradation rates fromsites in the Pacic Ocean. Caneld (1994) and Middelburg et al.(1997) present similar methods for determining the oxidationrate from u in the sea and Li et al. (2012) in lakes, and Burdige et al.(1999) developed a relationship between the organic matteroxidation rate and the DOM ux. The other important parameterswithin the rate laws are the Monod half saturation constants (KOxand KIn) in Approaches 1 and 3, and the limiting concentrations (LOxand LIn) in Approach 2, as described above. While these parameters

SCO2, SH2S and SBOH. In the advancement approach, the progressof all acidebase speciation reactions towards equilibrium is used

Some models include the ageing of iron and manganese

odeminerals from the more-reactive amorphous form to the less-reactive crystalline form (Table 5). The notation for more reac-tive (MnO2A, Fe(OH)3A) and less reactive (MnO2B, Fe(OH)3B) isconsistent across all Approach 2 papers, while one Approach 1paper uses the notation a and b (Reed et al., 2011b). The crys-talline phases do not react with organic matter, but they do reactwith

PH2S, and MnO2B oxidises Fe2. The inclusion and treat-

ment of pH and mineral transformations has no relation to theto calculate pH. The latter approach also allows transport of in-dividual species rather than lumped parameters, and thereforeallows implementation of species-specic diffusion coefcients.The advantages of these approaches are primarily compared as abalance between computation time and accuracy. Computationtime is minimised by reacting or transporting lumped species,whereas accuracy is maximised by reacting or transporting manyindividual species (Luff et al., 2001). Meysman et al. (2003b) addan acidebase equilibrium of the solid phase to the alkalinityconservation model. Most papers that calculate pH use the alka-linity conservation approach. Jourabchi et al. (2005) and Devalloiset al. (2008) focus specically on calculating pH proles indiagenesis models.have a slightly different use in the respective approaches, inspec-tion of the literature shows that values have been used inter-changeably between Approach 1 and 2 papers. For example, sevenApproach 1 papers source constants from the Approach 2 papersVan Cappellen and Wang (1996). However, Approach 3 constantsare consistently sourced from the original Approach 3 paper(Soetaert et al., 1996a).

3.2. Other chemical processes

3.2.1. Secondary redox reactionsThe subsequent reactions of chemical species produced by the

primary redox reactions (3)e(8) are referred to as secondary redoxreactions, and are usually given bimolecular rate laws that are rstorder with respect to the oxidant and reductant. Secondary re-actions in Approaches 1 and 2 include the oxidation of reducedspecies by oxygen and other reoxidation pathways, though theseare not always included and are quite variable depending on theapplication (Table 4). Approach 3 models treat these more simplyand include only the oxidation of ODU and NH4 by oxygen, in mostcases.

3.2.2. pH Control and mineral solubilityMany Approach 1 and 2 papers include ability for a calculated or

xed pH, but pH is not simulated in 26 papers, and it is not includedin the Approach 3 papers (Table 5). When pH is considered, it isoften calculated as a result of the reaction and transport of speciessuch as H2CO3, H2S, H3PO4, NH4 and B(OH)3. The fast, reversibleequilibrium reactions are in some cases calculated separately fromthe slower, kinetic organic matter oxidation reactions. Luff et al.(2001) discuss advantages and disadvantages of three methodsfor calculating pH in marine systems, comparing the charge bal-ance approach in CANDI (Boudreau, 1996) and the alkalinityconservation (or proton condition in Meysman et al., 2003a, b)approach in STEADYSED (Van Cappellen and Wang, 1996) with anequilibrium advancement approach (Luff et al., 2001). With thecharge balance approach, H concentration is calculated from thesum of all charged species, whereas in the alkalinity conservationapproach, H is calculated from total alkalinity, which is the sum of

D.W. Paraska et al. / Environmental M312treatment of primary or secondary redox reactions, and theminerals are typically chosen in any study are based on theenvironmental context and application.

3.2.3. Nutrients and adsorptionNumerous studies include nutrients (Table 6). Most generate

NO3 via oxidation of NH4 (nitrication; Table 4), and only Dhakarand Burdige (1996) include oxidation of NH4 by NO2, (anammox)despite this being a potentially important denitrication pathway(Lam and Kuypers, 2011). Some studies include the adsorption ofammonium to iron minerals, which makes it unavailable to livingorganisms (Table 6). Sohma et al. (2001, 2004, 2008) have a detailedtransport of organic PO43 through water column microorganisms.Several studies include acid/base reactions that change the speci-ation of H3PO4, while others allow PO43 to be adsorbed to partic-ulate metal phases (Table 6).

3.3. Physical and biophysical transport processes

3.3.1. Benthic faunaMost studies account for bioturbation by including constant

mixing down to a certain depth, with a decreasing amount belowthat. This decrease is calculated by a function applied to the bio-diffusivity (or bioturbation) term DB (see equations (1) and (2)).Many studies use depth-dependent exponential decay and t thefunction to the data according to their study site, while manyCANDI modellers use a function dependent on burial rate u. Therelationship between DB and u is generally explained on the basisthat a higher ux of organic matter will sustain a higher density ofbenthic macrofauna, as was tested statistically by Tromp et al.(1995) against 37 eld studies. Haeckel et al. (2001) required arange of bioturbation coefcients, based on radionuclide data oftheir study site. Due to the limits of the sediment diagenesis model,they applied a higher bioturbation rate with a lower organic matterux, though this does not reect the general understanding thathigher organic matter depositionwould support more bioturbation(Haeckel et al., 2001). Berg et al. (2003) and Fossing et al. (2004)suggest that DB should be assigned differently to solids and sol-utes, as bioturbation affects solutes much more than solids, and sothe coefcient could be around 10 times larger. However, few otherauthors (Kasih et al., 2008, 2009) have implemented separate DBvalues for solids and solutes.

The onset of hypoxic conditions can reduce or stop the activityof benthic animals, especially larger ones, and the return of oxicconditions, which causes the return or growth of animals, requiressite-specic information, as regions with a history of low O2 mayhave benthic organisms that have adapted to the conditions (Diazand Rosenberg, 2008). Soetaert and Middelburg (2009) usedifferent DB values for oxic and anoxic bottom water conditions.Fossing et al. (2004) account for bioactivity with an index (A) be-tween 0 and 1 for the rate of bioturbation as

DADt

KmA Kn1 A (13)

where Km is a potential rate of animal mortality, Kn a potential rateof growth, and the value of A is dependent on the amount of oxygenin the system. In periodically hypoxic waterways (Sohma et al.,2004, 2008), this is accounted for by making the bioturbation(D

0B) and bioirrigation (DI) coefcient dependent on the biomass of

deposit (DFB) and suspension (SFB) feeders, e.g.,:

D DFB SFB $D (14)

lling & Software 61 (2014) 297e325i DFB SFB HFi i max

odeTable 6Inclusion of nitrogen and phosphorus as nutrients in diagenesis models.

D.W. Paraska et al. / Environmental Mwhere i refers to either bioturbation or bioirrigation, HFi is a halfsaturation coefcient and Di max is the maximal coefcient of eitherbioturbation or bioirrigation. The concentrations of DFB and SFB areproportional to the dissolved oxygen concentration. Depending onthe growth rates, such formulations show the rate of recovery ofbenthic fauna biomass after reoxygenation, and a possible delay inthat recovery. In environments where eld studies show that irri-gation is a minor transport process, especially anoxic waterswithout macrofauna, the irrigation function is simply not used(Soetaert et al., 1998; Luff et al., 2000; Dale et al., 2009; Reed et al.,2011a). Detailed 3D transport models of irrigating worms havebeen developed (Meysman et al., 2006a, b, 2007) but are yet to beroutinely integrated with reactive transport models (see Meilelling & Software 61 (2014) 297e325 313et al., 2003 and Sochaczewski et al., 2008 for recent studies inthis area).

3.3.2. Resuspension of sediment particlesAn early coupled benthic-pelagic model by Wainright and

Hopkinson (1997) examined the effect of resuspension on aerobicoxidation of organic matter and denitrication in the sediment andwater column, however, this study was limited to a subset ofchemical reactions. There has not been the same adoption orexpansion of this approach over the last two decades as there waswith the diagenesis models, except for a recent study byMassoudieh et al. (2010) who demonstrate a full vertically-resolveddiagenesis model that also includes resuspension.

Table 7Application of diagenesis models to different environments with either steady or non-steady solutions.

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provides a useful starting point from which to consider theirtimescales, their coupling to the water column, and chemicaluxes in more detail.

4.1. Application environment

Here the studies are classied according to the nature of theenvironment in which the study was set: deep ocean, coastal,estuarine, riverine or lacustrine. Of the 83 studies inspected,coastal environments have received the highest number (35) ofapplications of sediment models, followed by the deep sea (17)(Table 7). One reason for the high number of coastal studies is thatlarge datasets have been collected at a few key sites, such as YoungSound and the Skagerrak. After 1996 when many new modelswere introduced, most deep ocean studies were published be-tween 1998 and 2002; most coastal studies were published from

D.W. Paraska et al. / Environmental Modelling & Software 61 (2014) 297e3253164. Applications

Next we highlight some of the practical issues involved in

Fig. 3. Plot of the range and median of kOM values, the maximum organic matterreaction rate coefcient. 2G-1 and 3G-1 are the most reactive fractions of 2- and 3-Gmodels, and 2G-2 and 3G-2 are the second-most reactive fractions of 2- and 3-Gmodels.applying a sediment diagenesis model that are not easily graspedby reading the theoretical resources (Table 7 provides an overviewof application approach). In general terms, early publicationsfocused on development of a new model code or simulated depthproles and surface uxes of the main chemicals involved in theearly diagenesis process, with focus on examining the t of modelresults to eld data, and establishing the sediment models as t forpurpose. Later publications have tended to target application ofthe models to a more specic research questions, by conductingbroad sensitivity analyses and examining system behaviour(Archer et al., 2002; Katsev et al., 2006a; Dittrich et al., 2009),while others have been more management oriented. An overviewof the application of the models in different environments

0 1 2 3 4 5 61995199619971998199920002001200220032004200520062007200820092010201120122013

Fig. 4. Number of publications each year per environment. 1996 stands out as the key yeapublished between 1998 and 2002, and most coastal studies from 1996.2002 onwards (Fig. 4). Marine studies (coastal and deep ocean)have been used to test the abilities of the models to reproduceeld measurements of depth proles and the associated chemicalreactions, with a focus on understanding biogeochemical cyclesrather than focussing on a specic applied problem.

In contrast, the 13 studies based in estuaries are much moretargeted at management-related questions, especially in terms ofrepresenting more complex hydrodynamics, spatial heterogene-ity and ecology, by coupling the sediment models to physicalmodels of the overlying water body and to ecological models (seebelow). Other differences to the marine studies are that most ofthe estuarine studies were published from 2004, 5 of the 13include DOM, and a one study (Bessinger et al.) included heavymetals.

Up to the late 1990s, the geochemistry and ecology of marinesediments had generally been studied more than freshwater sedi-ments (Boudreau, 1999); this is also true for the sediment diagen-esis modelling studies inspected here, where only 15 studies arebased in freshwater lakes and 4 in freshwater rivers. The moststriking contrasts between the freshwater lake studies and themarine studies are that 5 studies were motivated to model the uxof heavy metals, and no lake studies to date include dynamiccoupling to an ecological model or a spatially-resolved water col-umn model.

4.2. Steady state and dynamic simulations

Many diagenesis model papers refer to the concept of a steadystate, a term that applies to both the solution of the differentialequations and to the assumption about the condition of the

7 8 9 10 11 12

Deep seaCoastalEstuaryRiverLaker for publishing diagenesis model studies. After 1996, most deep ocean studies were

processes, but the solid substances are not. In some diagenesis

kinetic reactions (Smith and Jaffe, 1998; Luff et al., 2000). Once the

odesteady state has been calculated, a few models cease their simu-lation (for example, STEADYSED in Van Cappellen and Wang, 1996;Wang and Van Cappellen, 1996; Van den Berg et al., 2000) whereasmost use the steady state as an initial condition for time-dependentmodel papers, the difference between the observed and calculatedconcentrations is explained as a result of the inability of a steadystate model to capture dynamic changes in that environment,especially in the uppermost layers of the sediment (Boudreau et al.,1998; Haeckel et al. 2001; Wijsman et al., 2002; Canavan et al.,2006).

In theory, conditions in the deep ocean are more likely toresemble steady state than lake or coastal marine sediments, whereseasonal or episodic effects should be stronger and thereforeexternal conditions uctuate on early diagenetic timescales(Rabouille and Gaillard, 1991a; Gallon et al., 2004). However,Table 7 shows that in practice, simulations of deep-sea systems areequally likely to have been run at steady state or dynamically, whilesomewhat counter-intuitively more applications to freshwaterlakes have been assumed to be at steady state rather than dynamic.Seasonal changes are also considered more often in marine studies(5/17 in deep sea and 7/33 in coastal) than in estuarine (2/13) andfreshwater lakes (2/15).

4.2.2. Steady state as a numerical techniqueThere are two main numerical methods by which steady state is

reached. The most common method is to set the temporal deriva-tive to zero in the governing equations, then iterate the differentialequations until convergence, where the concentration change be-tween iterations is less than an error tolerance (106 in VanCappellen and Wang, 1996, and 103 in Benoit et al., 2006, or aresidual of 1014 in Rabouille and Gaillard, 1991a). Meysman et al.(2003b) refer to this as the steady-state calculation. The alterna-tivemethod is to solve the dynamic equations overmany time stepsuntil the concentration changes stabilise, known as an asymptoticrun (Meysman et al., 2003b). With constant boundary conditions,the main practical difference between the methods is that theasymptotic run is more computationally demanding. Some modelscan be run with a combination of both methods, with steady statecalculations for some kinetic reactions, such as organic matteroxidation, and a time-dependent solution for adsorption and othersedimentary environment. Steady state is where the concentrationsdo not change in time; the total inows and production are inbalance with the outows and consumption of all species.

4.2.1. Steady state as a description of the environmentSteady state can be a valid approximation when the changes at

the interface occur over a much longer timescale, such as a shift inclimate, or shorter timescale, such as bioirrigation, than the time ofresponse of thewhole system to aperturbation (VanCappellen et al.,1993). Deciding whether the system is at steady state depends onwhich sediment constituents are examined and the reference timescale. Generally, pore water responds to environmental changesfaster than the solid phase. Pore water solutes are transportedthrough the reactive part of the sediment over a fewmonths and sodo not reach steady state on a seasonal time scale, but can beconsidered at steady state on a decadal time scale (Pe~na et al., 2010).On the other hand, solids take decades or centuries to travel throughthe reactive sediment zone and so are at steady state on a seasonaltime scale but not a decadal time scale (Pe~na et al., 2010). Soetaertet al. (1996b) found that dissolved substances are at steady statewith respect to the instantaneous uxes of carbon mineralisation

D.W. Paraska et al. / Environmental Mcalculations with changing boundary conditions.The models with time-dependent calculations (Table 7) andchanging boundary conditions also adopt a range of approaches.Those that use the iterative steady state calculation can go througha series of successive steady states over time, which is the approachof Soetaert et al. (1996a), later taken up by authors such as Archeret al. (2002) andWijsman et al. (2002). The BRNSmodel, which waspartly developed from STEADYSED, has the capacity to use a similarapproach (Regnier et al., 2003; Aguilera et al., 2005; Thullner et al.,2005) or the asymptotic run (Canavan et al., 2006; Dale et al., 2009;Brigolin et al., 2009, 2011). Those that use the asymptotic methodspin up to a newasymptote over time.Within these, either a singleperturbation may be introduced (Wijsman et al., 2002; Talin et al.,2003; Katsev et al., 2006a), a stationary average of uctuations canbe set as the boundary (Fossing et al., 2004) or a uctuating quasi-steady boundary condition can be run, such as a pattern of seasonalchange (Luff and Moll, 2004; Kasih et al., 2008). The advantage ofusing the asymptotic method is that the time taken to respond tothe perturbation or the regular uctuation can be examined.

There is no pattern in the application of these techniques ac-cording to the groups used in the classication. Rather, in general,these models have developed to allow any combination of steady-state calculations, asymptotic runs, constant boundary conditions,perturbations or quasi-steady uctuations. While the options inearly studies were limited by the code of the model, most recentmodels provide the option of steady or time-varying conditions andthe choice can be made as to how the model is best applied to thestudy site.

4.3. Organic matter ux from the water column

The input of organic matter to the sedimentewater interface isone of the most important chemical inputs driving changes in thesediment (Tromp et al., 1995). Across the papers, there is a sur-prisingly large range of total organic matter inputs, which aremostly arrived at by calibrating the model against sediment depthprole data, usually total organic carbon or O2 depth proles.However, in a handful of cases, the studies have used sedimenttraps and SCO2 uxes (Berg et al., 2003; Fossing et al., 2004; Benoitet al., 2006; Katsev et al. 2006a; Kasih et al., 2008, 2009) whileothers predict the input with data and estimates based on primaryproduction (Reed et al., 2011b) or full water column models(Eldridge andMorse, 2000; Sohma et al., 2001, 2004; Eldridge et al.,2004; Morse and Eldridge, 2007; Brigolin et al., 2009; Pastor et al.,2011). Each environment shows a straightforward relationshipwithPOM uxes, which are generally smallest in the deep sea, as thedeep sea nutrient inputs are lower and more of the organic matteris oxidised in the water column before it reaches the sedimentsurface. The lowest total POM uxes, around 1 mmol cm2 y1, arefound in deep sea sites andmost of the highest uxes, around 1000,are found in the coastal sea. The quantities of these uxes arebroadly consistent with the estimates of Van Cappellen and Wang(1995) for uxes in each environment, suggested in the early daysof these models. For freshwater eutrophic lakes, however, there isno typical amount of lake sediment organic matter input.

In multi-G models, one of the more difcult parameters to sethas been the percentage of labile and refractory carbon, for whichthere is no simple experimental or theoretical guide. Of the fty-ve 2, 3 and 4 G models presented here, in 24 cases the diagenesismodel has been used to estimate the proportions of the fractions inthe ux to the sediments by back calculating from depth proles orsurface uxes (see Table 2). In eight cases the proportion is simplyassumed (ve of these are Approach 3) and in ve cases theamounts are estimated based on an empirical relationship to otherfactors such as sedimentation rate or primary productivity. Only

lling & Software 61 (2014) 297e325 317Benoit et al. (2006) estimate the uxes and proportions by using

odeuxes from a compilation of water column measurements at thesite itself. Those studies with lower amounts of labile organicmatter (where the most reactive fraction is less than 50% of theux) are mostly in near shore marine waters, coastal lagoons andone freshwater lake, which might reect a higher allochthonousinput from the catchment. However, many other coastal andfreshwater lake studies have much higher proportions of highlyreactive organic matter, so no typical labile-refractory ratio can bedistilled from the analysis in relation to environmentalcharacteristics.

4.4. Coupling to water column models

Most sediment models are one-dimensional with depth, whereone sediment column is used to represent an entire study site, or anidealisation of various representative sampling locations. Most ofthese have a simple water column boundary condition at the sed-imentewater interface, or a diffusive boundary layer. Conversely, inbiogeochemical water column models, the sedimentewater inter-face has usually been represented as a simple ux, resolved in one(Oguz et al., 2000; Shen et al., 2008; Lopes et al., 2010), two (Bruceet al., 2011) or three dimensions (see for example, Kiirikki et al.,2006; Xu and Hood, 2006; Kremp et al., 2007).

A fewsedimentdiagenesismodelling studies couple the sedimenttowater columnhydrodynamic and ecologymodels; rather than justa bottomwater boundaryat the sedimentewater interface, thewatercolumn is resolved with depth in one (Soetaert et al., 2001; EldridgeandMorse, 2008; Soetaert andMiddelburg, 2009), two (Benoit et al.,2006; Brigolin et al., 2011) and three dimensions (Sohma et al., 2001,2004, 2008; Luff and Moll, 2004; Smits and Van Beek, 2013). Luffand Moll (2004) undertook a thorough three-dimensional sed-imentewater modelling study where a spatially resolved model ofthe North Sea was used. The advantage of using a coupled model isthat both models are buffered by the dynamic feedback of the other,providing realistic forcing to the sediment. The studies by Sohmaet al. (2001, 2004, 2008) are dynamic three-dimensional modelsbased in estuaries, which examine the effects of oxic/anoxic uctu-ations in the water column on the sediment. While these estuarystudies have lower spatial resolution than in Luff and Moll (2004),they includemore complex ecologicalmodels and consider planktonand seagrass as sources of POM, DOM, nutrients and O2.

4.5. Applications to assess the effects of human activity

Beyond simply understanding the chemical processes in thesediment, some studies have been applied to assess the effects ofhuman activity onwaterways (Table 7). The models have been usedas predictive tools to assess management options: Canavan et al.(2006) predict the effect of opening up a freshwater coastal lagoonto the sea; Brigolin et al. (2009) use themodel to predict theeffects ofash farm in a fjord;Koniget al. (2001) predict theeffects of deep seamining on sea oor geochemistry; and Eldridge et al. (2004) predictthe effects of dredging and harmful algal blooms. They have also beused to examine the past drivers of water quality deterioration:Dittrich et al. (2009) examine the change of state in Lake Zug fromoligotrophic to eutrophic; Kasih et al. (2008, 2009) examine thedeterioration of the former pearl shery in Ago Bay; and Katsev andDittrich (2013) examine phosphorus uxes over decadal timescales.

Many of the studies have included nutrients (Table 6), which isessential for model studies examining eutrophication, however,models have rarely been used as a tool for examining contaminantux. There are many sediment reactive transport models that werenot within the scope of this analysis, which calculate heavy metaltransport in the sediment (for example, Gallon et al., 2004;

D.W. Paraska et al. / Environmental M318Carbonaro et al., 2005, see also the review by Boudreau, 1999)but few use the full diagenesis model to relate contaminants to thefate and transport of other sediment components.

5. Challenges and opportunities

5.1. Conceptualisation and measurement of organic matteroxidation

5.1.1. Reconnecting models to conceptual understandingSediment modellers have developed some elegant simplica-

tions of what they knew to be highly complex reaction processes,in order to reproduce commonly-observed sediment characteris-tics. It is shown above that the focus in the early period ofdevelopment was on establishing the organic matter oxidationprocess and its effects on redox zonation, whereas recentmodelling studies have focussed on applying the same or similarmodels to more specic chemical and ecological questions, aprogression that solidied the multi-G method as the standardpractice for diagenesis modelling. Despite the limits to the multi-G conceptual model, which were apparent in the earliest years ofits development, it was widely adopted because of its simplicity.The general process of organic matter oxidation used in mostmodels now involves one to three POM phases of different reac-tivity oxidising to CO2 through some of the reactions (3)e(8). Theoverall challenge seen when reviewing the sediment literature isthat these model structures have become increasingly separatedfrom laboratory and eld studies, which have in parallel led to thedevelopment of more rened conceptual models and classica-tion approaches for characterising organic matter groups andbreakdown rates.

One of the manifestations of the separation of the multi-Gmodelling studies from experimentally based studies is theassignment of the proportions of labile and refractory organicmatter, which in many cases is either adjusted to t eld data orsimply assumed, irrespective of the model approach or the envi-ronments in which the studies were based. The few studies thatinclude eld or laboratory data highlight the difculties inmeasuring these fractions, since measurable equivalents of eachfraction do not exist. One example of these differences is that lab-oratory studies have shown that aquatic organic matter generallybreaks down faster than terrestrial organic matter in the case ofmarine (Burdige, 2005), estuarine (Dai et al., 2009) and freshwater(Bastviken et al., 2004; Sobek et al., 2009) organic matter, yet this israrely explicitly considered in the model parameterisations.Another major difference between the numerical models and thelaboratory and eld studies is that only 13 of the 83 numericalmodelling papers include a DOMpool. This is despite the signicantbody of data that has been collected on sediment DOM (see, forexample, Hansell and Carlson, 2002; Schmidt et al., 2009) and thefact that DOM accumulated with sediment depth is one of thelargest pools of organic carbon globally (Hedges and Keil, 1995;Burdige, 2007). Understanding labile DOM mechanistically isimportant for understanding the reactive intermediates in thebreakdown of POM to CO2, and although refractory POM and DOMmay play a smaller part in the reaction processes, they both makeup the total organic matter prole and their local transport pro-cesses are quite different.

A further gap between the current modelling approaches andthe eld and laboratory data is the relatively common use in themodels of one value of kOM for all oxidants. This is despite severallaboratory studies that have reported signicantly different ratesthrough each of the six pathways (Westrich and Berner, 1984;Caneld et al., 1993; Arnosti and Holmer, 2003). There are alsomany studies that have compared the different rates of organic

lling & Software 61 (2014) 297e325matter breakdown under oxic and anoxic conditions (Kristensen

odeet al., 1995; Dai et al., 2009; Abril et al., 2010). The oxidation rate canalso change upon reoxidation after a period under anoxic bottomwater, and the rate can also depend on the duration of the previousanoxic period or priming (Aller et al., 2008; Abril et al., 2010). Theincreased oxidation rate upon reoxidation may be due to thepresence of chemical species such as H2O2, present only in oxicconditions, which are small enough to diffuse through large mo-lecular clusters (Bastviken et al., 2003). It is also known that organicmatter is preserved over the long term only under persistentlyanoxic conditions (Henrichs, 1995; Hedges and Keil, 1995; Burdige,2007); the preservation of organic matter may also occur throughthe processes of geopolymerisation (Hedges and Keil, 1995), sul-disation (only included in the diagenesis models of Dale et al.,2009 and Couture et al., 2010), interaction with iron (Lalondeet al., 2012) and adsorption of DOM. Berner (1995) foresaw DOMadsorption as a major potential addition to the multi-G model, yetto date it has only been used in two models (Sohma et al., 2004,2008; Massoudieh, 2010).

Van Cappellen et al. (1993) identied one of the obstacles tothe determination of precise rate constants as the lack of a set ofinhibition constants (KIn and LIn). The lack of data available forinhibition constants is partly a result of inhibition being animprecise theoretical concept used to explain redox zonation. Theorganic matter oxidation rate laws assume inhibition of all sub-sequent pathways when the oxidant concentration is above itsKOx or LOx. However, eld studies have shown that the pathwayscan often overlap, such as Fe3 reduction and SO42 reduction,denitrication and annamox, methanogenesis in the presence ofSO42, and SO42 reduction in the presence of O2 (Postma andJakobsen, 1996; Jakobsen and Postma, 1999; Caneld andThamdrup, 2009). Van Cappellen and Wang (1996) observe thatthe separation between processes is clearer in environments withlower net organic matter oxidation. We showed above that manyof the early models were designed for deep sea sites with a loworganic matter input, therefore the increasingly common ten-dency to apply the models to highly productive environmentsmay require further development of the conceptual model of theredox sequence. One possible clue to understanding the redoxzonation may come from the recent discovery of centimetre-longliving micro cables of bacteria that transport electrons betweenthe aerobic and sulphate-reducing zones (Pfeffer et al., 2012),which is also an exciting opportunity for diagenesis models toexplore.

Experimental biogeochemists have developed conceptualmodels of carbon pools and transformations that may serve as aguide for ongoing model development efforts. Models have beendesigned based on aspects such as molecular weight (forexample, Burdige and Gardner, 1998), partial equilibrium withhydrolysis, fermentation and respiration steps (Alperin et al.,1994; Lovley and Chapelle, 1995), and organic matter origin(Findlay and Sinsabaugh, 1999; Zonneveld et al., 2010). Bio-geochemists have also collected datasets of specic identiablemolecules in sediment organic matter and the calculated freeenergies of reaction (see for example, Amend and Shock, 2001;LaRowe and Van Cappellen, 2011; LaRowe et al., 2012), howeverthis data may be difcult to incorporate without making theconceptual model too reductive or the numerical model overlyparameterised. Designing a diagenesis model with DOM, adetailed organic matter breakdown sequence, bacterial biomassand thermodynamic factors, as well as the secondary reactionsand transport processes already in the main stream of models, isan exciting opportunity for future model development. Indeed,numerical models may be very useful tools for probing the manyinteractions that laboratory studies have identied through

D.W. Paraska et al. / Environmental Mtesting the relative performance of model structures of differentcomplexity, acknowledging that the sacrice of the multi-Gsimplicity could compensated with the gain of more renedpredictions of process rates.

5.1.2. Challenges of using experimentally-derived values forparameters

The need for a new conceptual model of organic matter oxida-tion is clearer whenwe consider the lack of experimentally-derivedparameter values, shown in the section on the choice of parametervalues. Moving away from some of the theoretical simplications ofthe multi-G model may make it easier to use laboratory or eldmeasurements as input or validation data for sediment diagenesismodels.

Many authors have identied the sheer lack of data availablefor determining the rate constants in biogeochemical modelsgenerally (Middelburg et al., 1997; Mooij et al., 2010; Pe~na et al.,2010). Boudreau (1999) writes that kinetic laws in sedimentmodels are largely educated guesses, because of the difculty inobtaining data without disturbing the natural sedimentary envi-ronment. The inherent difculty in measuring kOM in particular,the main rate constant for organic matter oxidation, comes fromthe spectrum of reaction rates that can span ten orders ofmagnitude, from minutes to 106 years under deep sea sediments.Any experiment to measure the rate will miss materials withbreakdown rates much shorter or longer than the observationtime span (Hedges and Keil, 1995). We have shown that there hasgenerally been a wide range of parameter values, most of whichhave been calibrated, which creates the risk that a set of theseconstants calibrated to one dataset might not be readily transfer-able to other study sites or models.

The transfer of the parameter values through the literaturewarrants further consideration since the range of environmentsand questions that the models are being applied to is widening eyet the values are still often taken from the original papers. Further,an Approach 1 or 2 study with its parameters tuned to a datasettypically has depth proles of only around 7 variables, which is stilltrue for papers published in recent years. Thus, although the scopeof the models has broadened, the collection of data for constrainingparameters or validating model processes has hardly increasedsince 1996.

Another risk is that the parameter set could be wrong, yetgenerate a good t to eld data e known as the problem of equi-nality (Luo, 2009). However, Van Cappellen and Wang (1996)argued that because diagenesis models have so many highlycoupled reactions, the range that the values could be calibratedwithin is in fact quite small. An error in one constant could possiblybe hidden by an error in another constant through the non-linearfeedbacks that shape the system, but it is unlikely that it could behidden through all of themany reactions. Therefore these guessesin diagenesis models are not necessarily unrealistic. Some diagen-esis modelling studies have conducted identiability analyses,which seek to show the sensitivity of model outputs to sets ofparameters, within which only some of the parameters are tted(Dittrich et al., 2009; McCulloch et al., 2013). Nevertheless, nomatter what the conceptual models of future sediment diagenesismodels will be, future endeavours to collect more specic and ac-curate determinations of process rates in situ will help us under-stand the range of uncertainty in our model simulations.

It must be emphasised that the sediment is a difcult environ-ment to collect data from and it is not a small task to collect aperfect eld dataset for a modelling study. Nevertheless, in situanalytical instruments have improved since the creation of thesediagenesis models in the 1990s, which may give us an opportunityto overcome the inherent difculty in measuring sediment data

lling & Software 61 (2014) 297e325 319(see reviews by Viollier et al., 2003; Moore et al., 2009). Sediment

odebiogeochemical measurements have been conducted with benthiclanders (see for example, Maerki et al., 2009; Sommer et al., 2010;Zhang et al., 2010), benthic chambers (see for example Chapmanand Van den Berg, 2005; Sommer et al., 2008; Ferron et al., 2008)and diffusive gradients in thin lms and diffusional equilibration inthin lms (see for example Jezequel et al., 2007; Monbet et al.,2008; Robertson et al., 2009). In combination with more rigorousperformance assessment using a wider range of metrics (e.g.,Bennett et al., 2013), modellers should ultimately be better able tojustify whether a model is t for purpose.

5.2. Opportunities to improve understanding of physical andbiological processes

5.2.1. Capturing the multiple scales of change affecting thesedimentewater interface

Another general challenge for sediment modellers is copingwith the different spatial scales, from the length of a study site tosediment pores, and the different scales of perturbation, fromseasonal oscillations to intense, one-off events. We showed abovethat there are only a few examples of depth-resolved sedimentmodels that are resolved horizontally, as part of a greater modellingsystem. At the large scale, most of these studies are based inestuarine and coastal environments, while freshwater lakes areunder-represented. The general lack of spatially-resolved modelshas occurred despite the benets that could be gained from higherresolution, such as the inclusion of specic physical and ecologicalfeatures of a study site or the ability to capture benthic-pelagicfeedbacks.

A deterrent to building spatially resolved models may be thelack of data at the appropriate spatial scale to calibrate the modelto, which could become less of a problem with the increasing so-phistication of eld instruments, as described above. Anotherdeterrent from adopting these models may be the perception thatspatial resolution requires signicant computation time. Forexample, a comparative study by Soetaert et al. (2000) concludedthat the best balance between model accuracy and computationalefciency for coupled water column models was struck when thesediment component was a simple ux term rather than a one-dimensional multi-layered sediment model. In the 13 years sincethat study, the computational efciency has increased substantially.Aside from only relying on the increasing processing power ofcomputers, the problem of long computation time can be mini-mised by separating the time step of the water column, which hasfaster transport, from the time step of the sediment. The sedimentcan also be divided into zones with a 2D resolution lower than thewater column resolution (as is done in Sohma et al., 2008 andBrigolin et al., 2011). Berg et al. (2007) have also addressed thegeneral problem of computation time in diagenesis models withoptions for faster numerical solution.

5.2.2. Using small-scale spatial resolution and reduced modelsAt a small scale, ne spatial resolution allows models to capture

variations such as localised deposition and the effects of bio-turbation. We have found a few examples of models where thesedetailed processes have been included, such as that inSochaczewski et al. (2008) andMuegler et al. (2012), which, like thelarge scale spatial models, are computationally demanding.Meysman et al. (2006b) compare 1D, 2D and a 3D bioirrigationtransport models, without any chemical reactions, and concludethat their 2D model gives the best balance between accuracy andsimplicity. The opportunity lies in creating reduced models (Rattoet al., 2012) with these ne-scale spatially-resolved models todetermine simple parameterisations that could then be used in

D.W. Paraska et al. / Environmental M320more computationally-demanding diagenetic model applications.5.2.3. Including resuspension of sedimentResuspension is well understood in physical models but rarely

used in biogeochemical models (Massoudieh et al., 2010). It is lessimportant in a calm water body such as the deep ocean, wheremany of the early sediment diagenesis modelling studies have beenbased, but as we have shown above, more studies are attempting tomodel shallower, higher-e